A problem of reconstructing a three-dimensional solid structure from a wire-frame has been widely studied and developed so far. Methods for reconstruction of the three-dimensional solid structure include a finding method using geometric information and a method using a graph theory etc. However, the conventional methods are applied only to triconnected graphs because an input wire-frame model is assumed to have an interpretation, i.e., an embedding determined in one-to-one correspondence to the input wire-frame model. Entire triconnected graphs form a subgroup of entire biconnected graphs, and generally require more dense geometrical connection relations, i.e., edges between vertices than the biconnected graphs. It is not ensured that the real wire-frame model satisfies the above assumption, and therefore the quite many restrictions are present in the conventional method which assumes the input graphs as triconnected ones. Since there are three-dimensional solids which may be categorized to the graphs other than biconnected or connected graphs, it is necessary to reduce the restriction in order to provide wide availability to a system used for actual computation of the real three-dimensional solids. In turn, there may be various interpretations for graphs other than triconnected graphs such as, for example, the biconnected or connected graphs, thereby providing another problem for providing wide availability to the three-dimensional designing.
The wire-frame model has been widely used in various fields, particularly in the field of a Computer Aided Design (CAD) system where three-dimensional geometry construction is necessary. In the three-dimensional geometry design field, sometimes a solid or a surface may be represented as a group consisting of curved segments. Such representations are not considered to be complete geometry representations because locations of surfaces are not clearly indicated. However, an exact interpretation of the solid is made possible when combined with knowledge of an operator on the subjected solid. Such the representation could be realized by aid of with such knowledge.
In a practical site of automated design using CAD systems, the process, first deciding the entire shape using characteristic curves represented as a wire-frame by a designer and then filling the wire-frame with all of adequate surfaces by another operator, is sometimes adopted. This procedure is adopted such that the designers working for highly sophisticated shape design are not troubled by time-consuming procedure for putting surfaces thereon or filleting thereof; the actual large CAD model sometimes requires several days for the latter portion.
The quite many wire-frame models have been used in past huge design data because a computing cost including memory capacity, CPU time, and restriction on a software for directly subjecting the curved surface to computation becomes high and operations to define the curved surfaces precisely become elaborate. Even in the present stage, since an operator may understand more easily geometrical elements having lower dimension, such wire-frames are used as an intermediate procedure in order to define surface geometry using specific surfaces in the geometry design.
An essential difference between the wire-frame models and solid models is that the latter includes a group of surfaces defining boundaries of the object. The group of the surfaces forms a closed shell which cooperatively encloses a finite volume. Therefore, in order to construct automatically the solid model from the wire-frame model, it is required first to interpret the entire wire-frame as a group of face loops with topological consistency and second to define curved surface within each of the face loop. However, when the three-dimensional geometry design is extended to handle the solid represented as biconnected graphs, the conventional three-dimensional geometry design procedure encounters the problem in which a plurality of interpretations for the given wire-frame are impossible as reviewed in the mathematical procedure described above.
Therefore, there are continuous needs to provide a method, a system, and a program product to interpret a given wire-frame model consisted from groups of curves in space as consistent face loops, even if the input wire-frame has a plurality of interpretations, which are not computed by conventional methods, and to reconstruct surfaces of the object corresponding to each of the face loop efficiently and accurately.